A modified Runge-Kutta method for increasing stability properties

被引：4
作者：
Hu, Guang-Da [1 ,2 ]
Wang, Zheng [2 ]
机构：
[1] Shanghai Customs Coll, Shanghai 201204, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 441卷
基金：
中国国家自然科学基金;
关键词：
Control theory; Nonlinear ODEs; Runge-Kutta methods; Increasing stability properties; Gradient; NONLINEAR CONTROL;
D O I：
10.1016/j.cam.2023.115698
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In control theory, we are interested mainly in investigating asymptotic stability of systems. In this paper explicit Runge-Kutta methods are investigated for numerical solutions of nonlinear ODEs with known strict Lyapunov functions. In order to increase stability properties, a modified version of explicit Runge-Kutta methods is presented. The modified Runge-Kutta method is explicit. It is different from the projection methods in literature which are implicit. Comparing with the standard Runge-Kutta method, the modified Runge-Kutta one has better stability properties. Numerical examples are provided to illustrate the effectiveness of the modified Runge-Kutta method.
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页数：8
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